This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A172011 #14 Apr 11 2024 18:18:17
%S A172011 0,12,24,72,192,528,1440,3936,10752,29376,80256,219264,599040,1636608,
%T A172011 4471296,12215808,33374208,91180032,249108480,680577024,1859371008,
%U A172011 5079896064,13878534144,37916860416,103590789120,283015299072,773212176384,2112454950912
%N A172011 a(n) = 12*A002605(n).
%C A172011 The case k=2 in a family of sequences a(n)=G(k,n), G(k,0)=0, G(k,1)=k*(k+4), G(k,n)=k*G(k,n-1)+k*G(k,n-2).
%C A172011 The Binet formula is G(k,n) = (c^n-b^n)*d where d=sqrt(k*(k+4)); c=(k+d)/2; b=(k-d)/2.
%C A172011 The generating functions are k*(k+4)*x/(1-k*x-k*x^2).
%C A172011 The case k=1 is A022088.
%H A172011 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,2).
%F A172011 Binet formula: a(n) = 2*2^n*((-1+3^(1/2))^(-n)-(-1)^n*(1+3^(1/2))^(-n))*3^(1/2) .
%F A172011 G.f.: 12*x/(1-2*x-2*x^2). a(n) = 2*a(n-1)+2*a(n-2).
%t A172011 LinearRecurrence[{2,2},{0,12},30] (* _Harvey P. Dale_, Mar 06 2023 *)
%Y A172011 Cf. A002605, A022088.
%K A172011 nonn,easy
%O A172011 0,2
%A A172011 Claudio Peruzzi (claudio.peruzzi(AT)gmail.com), Jan 22 2010
%E A172011 Edited and extended by _R. J. Mathar_, Jan 23 2010